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In: Statistics and Probability

A king and his army will attempt to capture a fortress. The left and right flanks...

A king and his army will attempt to capture a fortress. The left and right flanks break off from the main group to attack the west and east guard towers. Suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another.

If both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. If, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. If both flanks fail, then the king’s chance of capturing the fort drops to 20%.

It turns out the king captures the fort. What is the probability that one, and only one, flank was successful (either the left, or the right, but not both)?

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orchestra answered 2 years ago
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